Bolt Circle Calculator
This calculator works out the exact geometry of a bolt circle - the ring of equally spaced holes found on wheels, flanges, couplings and drilling jigs, commonly described by its pitch circle diameter (PCD). Enter the pitch circle diameter in millimetres, choose the number of bolts from the preset list of 2 to 12 or select custom for any other count, then set a start angle measured in degrees anticlockwise from the 3 o'clock position and, if needed, an X and Y offset to shift the circle's centre away from the origin. The calculator instantly returns the bolt radius, the chord length between adjacent bolt centres, the angular spacing between holes, and the circumference of the full circle, along with a table listing the angle, X and Y coordinates and distance from origin for every bolt hole, plus a scaled diagram showing the pattern. Use it to lay out hole positions for a drilling jig or CNC program, to check a wheel or flange bolt pattern such as 4x100 or 5x114.3, or to work backwards and find an unknown PCD from a measured chord length. All coordinates are calculated using standard trigonometry to four decimal places. Because this is a planning tool, always confirm critical dimensions with a calibrated vernier calliper or other measuring equipment before drilling or machining, and round the results to the tolerance your job actually requires.
1. Bolt Circle
2. Options
Bolt Hole XY Coordinates
| Bolt # | Angle (°) | X (mm) | Y (mm) | Distance from Origin (mm) |
|---|
Bolt circle diagram (not to scale)
How Bolt Circle Calculations Work
A bolt circle (also called a bolt pattern or pitch circle) is a circular arrangement of equally spaced holes used in flanges, couplings, wheels, and machinery. Given the pitch circle diameter (PCD) and the number of bolts N, the key values are:
- Radius (R): R = PCD / 2
- Angular spacing: 360 / N degrees between each hole
- Chord length: the straight-line distance between adjacent bolt centres = PCD × sin(π / N)
- XY coordinates of bolt i (0-indexed): x = cx + R × cos(start + i × 360/N), y = cy + R × sin(start + i × 360/N)
Angles are measured in degrees from the positive X axis (3 o'clock direction), increasing anticlockwise. You can shift the start angle to place the first bolt at any position, for example 90 degrees to put the first bolt at the top (12 o'clock).
Worked Example
Defaults: 6 bolts on a 100 mm PCD, start angle 0 degrees, origin at (0, 0).
- Radius = 100 / 2 = 50.00 mm
- Angular spacing = 360 / 6 = 60.00 degrees
- Chord length = 100 × sin(180 / 6) = 100 × sin(30°) = 100 × 0.5 = 50.00 mm
- Bolt 1 (0°): X = 50.00, Y = 0.00
- Bolt 2 (60°): X = 25.00, Y = 43.30
- Bolt 3 (120°): X = -25.00, Y = 43.30
- Bolt 4 (180°): X = -50.00, Y = 0.00
- Bolt 5 (240°): X = -25.00, Y = -43.30
- Bolt 6 (300°): X = 25.00, Y = -43.30
Common Bolt Patterns
| Application | Pattern | Typical PCD | Chord Length |
|---|---|---|---|
| Car wheel (small) | 4x100 | 100 mm | 70.71 mm |
| Car wheel (large) | 5x114.3 | 114.3 mm | 67.19 mm |
| Car wheel (truck) | 6x139.7 | 139.7 mm | 69.85 mm |
| Industrial flange DN50 | 4x | 125 mm | 88.39 mm |
| Industrial flange DN100 | 8x | 180 mm | 68.88 mm |
How to Measure PCD on an Existing Part
If you need to find the PCD of an existing bolt pattern, measure the distance between the centres of two adjacent bolt holes using a vernier calliper. Then use the formula: PCD = chord / sin(π / N). For example, if you measure 50 mm between adjacent holes on a 6-bolt pattern: PCD = 50 / sin(30°) = 50 / 0.5 = 100 mm. For a 4-bolt pattern, measure the centre-to-centre distance of two diagonally opposite bolts; that distance is equal to the PCD.
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Method: Standard bolt circle trigonometry. Coordinates: x = cx + (PCD/2) × cos(θ), y = cy + (PCD/2) × sin(θ) where θ = start_angle + i × (360/N) in degrees. Chord length = PCD × sin(π/N). All values computed in double-precision floating point.
This calculator is for planning and reference purposes. Always verify dimensions with calibrated measuring equipment before machining or fabrication. Coordinate precision is to 4 decimal places; round to your required tolerance for workshop use.